Search results for "Fractal"
showing 10 items of 329 documents
Fractal dimension: A useful tool to describe the microgeometry of machined surfaces
1993
Abstract The authors have utilized some concepts of fractal geometry to describe the complexity of profiles surveyed from surfaces worked by cutting. In particular an experimental analysis was carried out to investigate the influence of the worked material, cutting speed and cutting operation on the “fractal dimension” parameter. The obtained results show that this parameter is able to describe the irregularities of the profile on a small scale, which is important for an overall understanding of the functional behaviour of machined surfaces. Such descriptions cannot be derived from the more commonly employed parameters.
La relativité d’échelle dans la morphogenèse du vivant : fractal, déterminisme et hasard
2012
The Scale Relativity Theory has many biological applications from linear to non-linear and, from classical mechanics to quantum mechanics. Self-similar laws have been used as model for the description of a huge number of biological systems. Theses laws may explain the origin of basal life structures. Log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps. The existence of such a law does not mean that the role of chance in evolution is reduced, but instead that randomness and contingency may occur within a framework which may itself be structured in a partly statistical way. The scale relativity th…
Lévy-type diffusion on one-dimensional directed Cantor graphs.
2009
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity and the mean square displacement as a function of the topological parameters of the sets. Interestingly, the systems undergoes a transition from superdiffusive to diffusive behavior a…
The fractal model of non-local elasticity with long-range interactions
2010
The mechanically-based model of non-local elasticity with long-range interactions is framed, in this study, in a fractal mechanics context. Non-local interactions are modelled introducing long-range central body forces between non-adjacent volume elements of the elastic continuum. Such long-range interactions are modelled as proportional to the product of interacting volumes, to the relative displacements of the centroids and to a distance-decaying function that is monotonically-decreasing with the distance. The choice of the decaying function is a key aspect of the model and it has been proved that any continuous function, strictly positive, is thermodynamically consistent and it leads to …
Differentiation of hepatocellular adenoma by subtype and hepatocellular carcinoma in non-cirrhotic liver by fractal analysis of perfusion MRI.
2022
Abstract Background To investigate whether fractal analysis of perfusion differentiates hepatocellular adenoma (HCA) subtypes and hepatocellular carcinoma (HCC) in non-cirrhotic liver by quantifying perfusion chaos using four-dimensional dynamic contrast-enhanced magnetic resonance imaging (4D-DCE-MRI). Results A retrospective population of 63 patients (47 female) with histopathologically characterized HCA and HCC in non-cirrhotic livers was investigated. Our population consisted of 13 hepatocyte nuclear factor (HNF)-1α-inactivated (H-HCAs), 7 β-catenin-exon-3-mutated (bex3-HCAs), 27 inflammatory HCAs (I-HCAs), and 16 HCCs. Four-dimensional fractal analysis was applied to arterial, portal v…
Twin axial vortices generated by Fibonacci lenses.
2013
Optical vortex beams, generated by Diffractive Optical Elements (DOEs), are capable of creating optical traps and other multifunctional micromanipulators for very specific tasks in the microscopic scale. Using the Fibonacci sequence, we have discovered a new family of DOEs that inherently behave as bifocal vortex lenses, and where the ratio of the two focal distances approaches the golden mean. The disctintive optical properties of these Fibonacci vortex lenses are experimentally demonstrated. We believe that the versatility and potential scalability of these lenses may allow for new applications in micro and nanophotonics.
Organic fractal nano-dimensional structures based on fullerene C60
2019
The ways for a synthesis of nanoporous and close-packed types of fullerene C60 aggregates in two-component organic solvents (toluene + tetrahydrofuran) were established as well as their structural ...
F-signature of pairs: Continuity, p-fractals and minimal log discrepancies
2011
This paper contains a number of observations on the {$F$-signature} of triples $(R,\Delta,\ba^t)$ introduced in our previous joint work. We first show that the $F$-signature $s(R,\Delta,\ba^t)$ is continuous as a function of $t$, and for principal ideals $\ba$ even convex. We then further deduce, for fixed $t$, that the $F$-signature is lower semi-continuous as a function on $\Spec R$ when $R$ is regular and $\ba$ is principal. We also point out the close relationship of the signature function in this setting to the works of Monsky and Teixeira on Hilbert-Kunz multiplicity and $p$-fractals. Finally, we conclude by showing that the minimal log discrepancy of an arbitrary triple $(R,\Delta,\b…
Quantum systems with fractal spectra
2002
Abstract We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection and show strict connections between the decay properties of the states in the singular subspace and the algebraic number theory. More specifically, we study the decay properties of free n-particle systems and the computability of decaying and non-decaying states in the singular continuous subspace.
The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities
2015
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (g…